Student/Teacher Ratios

Below I analyze data from UNESCO’s Institute of Statistics, the World Development Indicators Database (WDI), and evaluate the impact of student-teacher ratio’s on education taking into context different levels of wealth. The UNESCO data can be found here, and the WDI data can be imported easily with the following code

library(WDI)
WDIsearch("public.*education") %>%
  as.data.frame() %>%
  tbl_df() %>%
  arrange(str_length(name)) %>%
  View()

1 Data Exploration

First I separate the data into two different type: primary education, and secondary education. First I investigate primary education:

It appears that student/teacher ratio is negatively correlated with country wealth, both per capita and total. There are, however, some exceptions - the US, UK, and Switzerland do not have low student/teacher ratios, while relatively low income countries like Cuba, Greece, and Georgia do have lower ratios.

The distribution of student-teacher ratio has a slight right skew, and is almost bimodal.

1.1 Country Per Capita Wealth vs. Student/Teacher Ratio

There is clearly a negative correlation between a country’s wealth and its student/teacher ratio.

1.2 What Other Indicators Have an Impact?

There’s a bunch of other factors to test from WDI data, literacy has an obvious negative association with student-teacher ratio which is likely also strongly associated with country wealth, and secondary school enrollment follows the same logic showing a steady rate of increase with GDP per capita. Finally, looking at secondary school enrollment and student/teacher ratio, wealth appears to play the biggest roll again as there is significant negative association, but most countries clustered in the upper left are once again at the top of most GDP per capita rankings (PPP adjusted or otherwise).

2 Models and Post Hoc Analysis

2.1 Linear Regression

I developed a couple simple models just to get a numerical idea of the data, for each 1% increase in secondary enrollment a 0.449 decrease in student-teacher ratio is expected, and for each 1 point increase in GDP per capita a 6.817 point decrease in the student-teacher ratio is expected.


	Student Ratio
	(1)	(2)

Secondary Enrollment	-0.449^***
	(0.029)

GDP Per Capita (US)		-6.817^***
		(0.449)

Constant	54.652^***	82.003^***
	(2.203)	(3.960)

N	100	139
R²	0.708	0.627
Adjusted R²	0.705	0.624
Residual Std. Error	7.115 (df = 98)	7.647 (df = 137)
F Statistic	237.222^*** (df = 1; 98)	230.305^*** (df = 1; 137)

Notes:	^***Significant at the 1 percent level.
	^**Significant at the 5 percent level.
	^*Significant at the 10 percent level.

Examining the confounding variable:


	Secondary Enrollment

Student Ratio	-0.985^***
	(0.178)

GDP Per Capita (US)	6.482^***
	(1.597)

Constant	36.974^**
	(17.543)

N	98
R²	0.748
Adjusted R²	0.743
Residual Std. Error	12.479 (df = 95)
F Statistic	141.256^*** (df = 2; 95)

Notes:	^***Significant at the 1 percent level.
	^**Significant at the 5 percent level.
	^*Significant at the 10 percent level.

2.2 Primary vs. secondary education

A work by Duncan Gates

gatesdu@oregonstate.edu